Teaching a neural network to play a card game with two phases
I've played this game. If I remember correctly, a successful strategy (for winning as many tricks you estimated to win) involves continually evaluating how well you're doing. If you're doing very poorly relative to your initial estimation, that's valuable information to have.

I think you should have one network that outputs--at every time step--both an estimate of future tricks won and an action of which card to play. This has the additional advantage of giving you more estimation experience with which to train. After all rounds, you'll know how far off each of your estimations were throughout the game. This should speed up learning on that part of the game.